Graphs can be reflected by applying negative values to a function.

If the negative value is applied *before* the function takes place, then the result is a reflection in the *y*-axis.

If the negative value is applied to the *result* of the function, then the reflection will take place in the *x*-axis:

Sketch the graph of the function `f(x)=x^2`. On the same graph, sketch `-f(x)`.

Describe the transformation.

A negative value applied *after* the function is evaluated will reflect the curve in the `x`-axis.

Answer: The curve is reflected in the `x`-axis.

Sketch the graph of the function `f(x)=x^2`. On the same graph, sketch `f(-x)`.

Describe the transformation.

A negative value applied *before* the function is evaluated will reflect the curve in the `y`-axis.

Answer: The curve is reflected in the `y`-axis.

See also Expressions as Functions and Reflection

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